It’s not mandatory, it’s a way to put emphasis on the subject, most probably because there was previous mention of a rejected law proposal. It’s always a pronoun which is used for the repetition and it is the emphasized form (moi, toi, lui, eux instead of je, tu, il, ils). Personally, I’d have put the elle between comas:

La proposition de loi Cispa a, elle, été adoptée par la Chambre.

Note that it’s something different than the repetition of the subject, common, sometimes mandatory, in questions. There, one expect the subject to be after the verb but in some cases, for instance when the subject is too complex, the subject is before the verb and a pronom-de-reprise repeat it after.